On nilpotent groups of automorphisms with fixed-point-free action

1972 ◽  
Vol 23 (1) ◽  
pp. 232-235 ◽  
Author(s):  
Jeremy Wilson
Keyword(s):  
Fixed Point ◽  
Free Action ◽  
Nilpotent Groups ◽  
Point Free Action ◽  
Groups Of Automorphisms

scholarly journals Fixed point free action on groups of odd order

2008 ◽  
Vol 320 (1) ◽  
pp. 426-436 ◽  
Author(s):  
Gülin Ercan ◽  
İsmail Ş. Güloğlu
Keyword(s):  
Fixed Point ◽  
Free Action ◽  
Odd Order ◽  
Point Free Action

scholarly journals Fixed Point Free Action with Some Regular Orbits

1997 ◽  
Vol 194 (2) ◽  
pp. 362-377 ◽  
Author(s):  
Alexandre Turull
Keyword(s):  
Fixed Point ◽  
Free Action ◽  
Point Free Action

Fixed-point free action of an abelian group of odd non-squarefree exponent

2011 ◽  
Vol 54 (1) ◽  
pp. 77-89 ◽  
Author(s):  
Gülin Ercan ◽  
İsmail Ş. Güloğlu ◽  
Öznur Mut Sağdiçoğlu
Keyword(s):  
Fixed Point ◽  
Finite Group ◽  
Abelian Group ◽  
Solvable Group ◽  
Free Action ◽  
Finite Solvable Group ◽  
Fitting Length ◽  
Point Free Action ◽  
A Finite Group

AbstractLet A be a finite group acting fixed-point freely on a finite (solvable) group G. A longstanding conjecture is that if (|G|, |A|) = 1, then the Fitting length of G is bounded by the length of the longest chain of subgroups of A. It is expected that the conjecture is true when the coprimeness condition is replaced by the assumption that A is nilpotent. We establish the conjecture without the coprimeness condition in the case where A is an abelian group whose order is a product of three odd primes and where the Sylow 2-subgroups of G are abelian.

A GENERALIZED FIXED-POINT-FREE ACTION

2012 ◽  
Vol 12 (03) ◽  
pp. 1250172
Author(s):  
İSMAİL Ş. GÜLOĞLU ◽  
GÜLİN ERCAN
Keyword(s):  
Fixed Point ◽  
Finite Group ◽  
Solvable Group ◽  
Upper Bound ◽  
Prime Order ◽  
Free Action ◽  
Group A ◽  
Point Free Action ◽  
A Finite Group ◽  
Coprime Order

In this paper we study the structure of a finite group G admitting a solvable group A of automorphisms of coprime order so that for any x ∈ CG(A) of prime order or of order 4, every conjugate of x in G is also contained in CG(A). Under this hypothesis it is proven that the subgroup [G, A] is solvable. Also an upper bound for the nilpotent height of [G, A] in terms of the number of primes dividing the order of A is obtained in the case where A is abelian.

On nilpotent groups with close groups of automorphisms

1974 ◽  
Vol 13 (5) ◽  
pp. 306-311 ◽  
Author(s):  
G. A. Noskov ◽  
V. A. Roman'kov
Keyword(s):  
Nilpotent Groups ◽  
Groups Of Automorphisms
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